As mentioned in Section REF , we can show that
the running time of the algorithm in [1]} is \(O(\chi ^2 + n\cdot \eta \cdot \chi \cdot |\Pi |)\) .
Here, \(\chi \)  is the number of face-edge paths \(\pi \)  of \(\Pi \)  with \(\phi (\pi )\notin \Gamma (\pi )\) , and
\(\eta \)  is the maximum length of \(\bar{f}\)  for all initial functions \(f\) .The definition of the initial functions is given in Section REF .
The value of \(\chi \)  is \(2^{O(k)}\cdot \textsf {MaxDeg}\) , where \(\textsf {MaxDeg}\)  denotes
the maximum degree in \(G\)  of the vertices on the frames and skeleton forests.
At this point, \(\textsf {MaxDeg}\)  can be as large as \(\Theta (n)\) .
